This invention relates generally to a method and systems for evaluating embedded options of structured-finance securities, and, more particularly, to the process of reducing theoretical financial engineering methods to computational instructions.
Commercial mortgage-backed securities (CMBS) are a subset of a class of financial securities known as asset-backed or structured-finance securities. CMBS are bonds of various seniorities, whose payments are made from the cash flows obtained from a CMBS trust. A CMBS trust is a legal entity that consists of a collection of loans secured by commercial real estate loans (CRELs) called the underlying loan pool. These CREL's are usually fixed-rate loans of a particular maturity, although they can include floating-rate loans as well. The properties securing these loans are usually diverse, both geographically and economically. Issued against the cash flows of the CMBS loan pool are a collection of bonds. These bonds are usually fixed-rate with a given maturity. Different classes of bonds are issued (called bond tranches) with different seniorities relating to the timing of the cash flows from the loan pool. The most senior bonds get the cash flows before the less senior bonds do, including any prepayment of principal. Principal repayment can occur due to voluntary prepayments or recoveries in the event of default. In reverse order to seniority, the least senior bonds lose their underlying principal first from defaults. In addition, most CMBS trusts issue a class of bonds called interest-only (IO) bonds, whose cash flows come solely from the interest payments to the loan pool, but only after all the senior bond coupons are paid. IO bonds receive no principal payments from the loan pool. The cashflow allocation from a typical CMBS capital structure can be found in FIG. 1.
The collateral for CMBS are mortgages secured by commercial (income producing) properties such as Multifamily, Hotel, Office, Retail & Industrial.
The majority of CMBS are bonds in a senior/subordinated sequential-pay structure. In a senior/subordinated sequential-pay structure the principal (prepays or scheduled amortization) and interest payments from the loan collateral in the trust flow sequentially from the top to the bottom of the capital structure beginning with the AAA class A-1 down thru to the Unrated Class J in accordance with the rules established for the deal.
As the principal amounts of each of the individual classes pay off (A1 Balance=$0), then the next bond in the sequence (from top to bottom) begins to receive principal payments, until it is paid down, etc., (A2 Balance=$0); Principal payments (including all prepayments); i.e., a top-down approach.
Principal losses are created by defaults in which the recoveries from the disposition of the securing property are of an amount insufficient to cover the outstanding balance on the mortgage. Such losses to the trust are allocated to the lowest rated class outstanding at the time of the loss in reverse, sequential payment (i.e., Class J gets losses until J Balance=$0, then. Class I gets losses until I Balance=$0, etc., i.e., a bottom-up approach.
Although the CMBS Universe contains a variety of transaction types, including Single Asset Transactions (1 loan) and large loan transactions (typically 5-15 loans), diversified conduit transactions are the most common type of CMBS transaction. A typical conduit transaction is structured using a CMBS trust that contains around 100 underlying loans (typically first liens), and issues about 10 different bond tranches, including an IO bond. There are over 650 CMBS trusts and, thus, over 6,500 CMBS constituting the CMBS universe trading over-the-counter across both fixed-rate and floating-rate collateral, including both US and foreign collateral. In addition to traditional CRELs discussed above, CMBS trusts often contain credit tenant leases (CTLs). CTLs are first liens that are guaranteed by either a rated corporate entity or a non-rated borrower who provides guarantor status through certain lease provisions (triple-net lease, double-net lease, etc. . . . ) Because rated CTLs benefit from a corporate guarantor, the likelihood of their default must be associated with the overall likelihood of default of the rated corporate guarantor and not based upon its CREL characteristics. In contrast, unrated CTLs are treated as traditional CRELs, because the non-rated borrower guarantor information is unavailable.
The CMBS sector is the most complex member of the structured finance product family, which, at $400 billion, represents about 10% of the entire $4.0 Trillion structured finance universe. Despite the size of this market, CMBS and CREL investors do not enjoy the benefits of financial engineering risk-management technology that is applied to more mature, but fundamentally less complex, securities such as Residential Mortgage-backed Securities (“RMBS”).
The collateral underlying RMBS are mortgages secured by residential properties. In order to receive the payment guarantees of interest and principal from the government and quasi-government agencies, GNMA, FNMA, and FHLMC (together, the “Agencies”), such mortgages must satisfy the underwriting and pooling requirements established by the Agencies. These requirements relate primarily to size of mortgage, leverage amounts, coupon and geographic distribution, and servicing fees and rights and have been established to provide investment banking underwriters and professional investment managers with a level of comfort surrounding the homogeneity and transparency of the collateral securing RMBS. The majority (approximately 80%) of RMBS are secured by collateral satisfying the requirements established by the Agencies (the “Agency RMBS”); the remaining RMBS that do not satisfy the Agencies' requirements are referred to as Non-Conforming, Jumbo, or Whole-Loan RMBS (approximately 20%). Because residential mortgage borrowers may freely prepay their mortgages without economic penalty or restriction, and because the Agencies guarantee the payment of principal to bond holders, thereby eliminating the risk of losses of principal due to default, investors in RMBS are primarily concerned with prepayment risks and the timing uncertainties associated therewith. Addressing this single concern ultimately gave rise to the development and subsequent ubiquitous use of Option Adjusted Spread (“OAS”) methodologies for this $2.0 trillion market segment. OAS provides investors with a single reliable measure to evaluate the impact of the underlying borrower's option to prepay a mortgage on the value of any Agency RMBS.
Prior to the introduction of OAS, the Public Securities Association (“PSA”, but now the Bond Market Association, “BMA”) attempted to address the RMBS investor's concern about the uncertainty of prepayments by requiring that every RMBS issuer price all Agency RMBS by using the “PSA Curve,” shown in FIG. 2, to estimate prepayments on a given collateral pool. This PSA Curve is still used today to price RMBS at issuance and to report the monthly rate of prepayment (also known as prepayment speeds) to investors. The application of the PSA Curve is straightforward: At 100% of the PSA Curve, all loans within a pool are assumed to partially prepay in an amount equal to 0.2% (on an annualized basis) of their outstanding principal balance at the beginning of every month for the first 30 months and then are assumed to prepay at constant rate of 6% (on an annualized basis) for the remainder of the lives of each of the loans in the pool. Increases or decreases to the PSA Curve are linear so, for example at 200% of the PSA Curve, all loans are assumed to prepay at 0.4% for the first 30 months and then are assumed to prepay at constant rate of 12% for the remainder of the lives of each of the loans in the pool—for 50% the loans are assumed to prepay at 0.1% for the first 30 months and 3% for the remainder of the lives of each of the loans in the pool, and so forth.
The standard and required use of the PSA curve is an explicit acknowledgement that the principal payment schedules of collateral securing RMBS have embedded prepayment options whose strike prices are unknown. It should be noted that no such established PSA curve exists, or has ever existed, for either CMBS or CRELs to date.
As a single-path/static estimate of prepayments, the PSA curve was imprecise and limited as a bond valuation tool. As a result, this estimation rapidly gave way to the introduction and adoption of highly quantitative theory and sophisticated computer technology to derive better, multi-path, forward-looking measures of prepayment risk. Over the past twenty years, practitioners and theoreticians have implemented robust modeling procedures involving interest rate diffusion processes and simulation of random walks to be mapped against simulated cashflows of the underlying pools to quantify in a precise and repeatable way the risk of prepayment underlying RMBS using OAS Methods based on stochastic processes. Today, OAS risk measures are derived by several third-party research firms as well as all major investment banks in the United States. The following statement on OAS for RMBS by an expert in the field of mortgage-backed securities research, Dr. Lakhbir Hayre—Managing Director of Salomon Smith Barney's Mortgage Research Group (from his book Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities), is worth noting:                OAS methodology, while not perfect, does provide substantial insight for RMBS investors, which may result in improved security selection (buy/sell) and overall improvement in returns realized by professional portfolio managers . . . . In the relatively short time since its development, OAS analysis became an essential tool for MBS investors. Its widespread acceptance indicates that most investors are well aware of the optionality inherent in RMBS . . . OAS has been derived as an extension of the standard spread over treasuries (yield to maturity), to account for the dispersion and uncertainty associated with the return of principal from RMBS. Can it be realized as a return over treasuries? Theoretically, with dynamic hedging, the answer is yes . . . From a practical point of view, however, it is perhaps best to think of the OAS . . . as a useful measure of relative value . . . (V)arious studies have shown that, applied consistently over time, OASs can be good indicators of cheap or rich RMBS″ (Hayre, Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities, 2001, pp. 39-40)        
One such study was conducted by Hayre for Salomon Brothers in the early days of OAS in the RMBS market. The study of RMBS spanned the period from 1985 to 1990 and compared the use of OAS methods to discern risk versus the traditional yield to maturity method. The use of OAS resulted in a 21% improvement in the frequency of positive returns over the yield to maturity method and an average periodic outperformance of 174 basis points (1.74%) on an annualized basis over the 5-year period of that study. In only 8% of the cases did yield to maturity provide better returns than OAS. Finally it is worth noting anecdotally that during the period of this study there were substantial increases in the issuance of RMBS, which can be partially attributed to increased confidence on the part of mortgage bankers in their ability to hedge their mortgage issuance pipeline risk of prepayment using OAS methods. This increased confidence in the ability to measure prepayment risk on a forward looking basis is widely regarded by experts in the literature as a significant catalyst for more favorable mortgage rates, which, in turn, reduced the prospective American homeowner's prospective mortgage payments, thereby increasing American home ownership by making it more affordable. The application of OAS to RMBS, therefore, was an important part of the rationalization of the lending market enabling mortgage bankers to hedge prepayment risk in the lending pipeline more efficiently, enabling them to lend at more competitive rates which, ultimately, significantly contributed to the creation of a more efficient housing market throughout the United States
The structural complexity of CMBS and the heterogeneity of the CRELs underlying such CMBS have provided a significant barrier to the development of a robust financial theory that accurately addresses the substantial risks of prepayment and default on both the CRELs and CMBS. In a typical CMBS trust there are CRELs secured by different property types (multifamily, retail, hotel, industrial, and office, among others) in different geographic regions (Downtown NYC—Office, Houston, Tex.—Multifamily, Tempe Arizona—Hotels, etc) throughout the United States. Additionally, each of these loans has different amounts of leverage (as measured by the loan to value ratio (“LTV”) at issuance—70%, 90%, etc.) and differing amount of income support for such leverage (as measured by the Ratio of the Commercial Real Estate (“CRE”) property's net operating income to the annual mortgage payment on the CREL secured by such property—a.k.a. the debt service coverage ratio (“DSCR”)—1.35×, 2.83×, etc.). Since the principal payments of CMBS and CRELs are generally not guaranteed by government agencies, these financial objects expose investors to both prepayment and credit risk. (One exception in CMBS is FNMA Designated Underwriter Servicer (FNMA-DUS) bonds which are backed 100% by first liens on multifamily properties. Like conforming RMBS, FNMA-DUS CMBS do carry the guarantees of interest and principal. FNMA-DUS constitute less than 10% of the CMBS market.) Thus, to value a CMBS bond accurately, one must first understand the cash flows to the underlying CMBS loan pools, the cash flow allocation rules to the various bond tranches, the prepayment restrictions/penalties, and the credit profile of the trust based on the underlying CRE collateral. The valuation of CMBS therefore must include a robust treatment of four significant risks-market, credit, prepayment and liquidity.
Prior to the development of the process of this invention, there existed significant intellectual barriers to understanding credit risk because this discipline has only become mature over the past few years; in addition, the significant financial barriers to the securing of computational hardware and software necessary to compute the voluminous number of paths needed to adequately simulate the risks of CRELs have impeded previous efforts to develop a model for the evaluation of the risks of CMBS and the underlying CRELs. Moreover, during the economic boom of the mid- to late-1990s, credit issues were not a major concern for many risk managers involved in CMBS; property prices were rising steadily from the levels that were depressed during the recession of the early 1990s, and the prospect of experiencing default on CRELs seemed, with good reason, remote. As a result, less than robust forms of risk-management evaluation proved satisfactory for the developing CMBS market. Today, the risk measurement technologies available to professional. CMBS investors remain effectively at the level of those available to RMBS investors in the early to mid-1980's: yield to maturity and spread to treasuries (and swaps) are used by market participants as the sole quantifiable and repeatable measures of risk and reward in conjunction with measures of tenor such as duration and weighted average life by market participants.
The economic downturn experienced since early 2000 has revealed weaknesses in the risk-management practices of many of the world's largest financial institutions in the areas of hedging and underwriting structured finance securities, especially with regard to CMBS and CRELs. The threat of actual default and the liquidity crisis and associated price volatility during October 1998 and September 2001 exposed weaknesses in banking and trading practices related to CREL and CMBS. The lack of adequate risk management tools in these times of stress exposed investors in CMBS and CRELs to substantial losses, even in the absence of actual defaults. Moreover, in response to trading, banking, and accounting losses incurred by financial institutions involved in the CMBS and CREL markets, the Basel Commission is considering imposing capital requirements in the Basel II Accord that will significantly restrict the levering, lending, and investment practices of major financial institutions in the area of CMBS and CRELs. Thus it has become clear that better risk management technology is necessary for CREL and CMBS markets to continue to function efficiently.
The closest attempt to derive any measure of risk of the collateral pool underlying CMBS resides with the public securities rating agencies (S&P, Moody's, and Fitch), However, the rating agencies only scientifically analyze the fundamental credit risk of CRELs underlying CMBS at issuance and make no claims regarding risks associated with the price volatility of CMBS in the secondary marketplace. Further, the rating agencies make no claim as to the prepayment exposure of CMBS investors. So, while rating agencies provide valuable ongoing monitoring of collateral pools and frequently upgrade and downgrade securities according to their internal rating system, the ratings and subordination levels generated by the rating agencies are inappropriate metrics of risk for professional investors, because they do not quantify the relative value of securities.
Since Dec. 11, 2003, several vendors (including the rating agencies) have made available to the market software that employs deterministic/forecasting models to impute the Probability of Default, Loss Given Default, Exposure at Default, and Maturity at Default of CRELs. Such deterministic/forecasting models do not provide non-deterministic theoretical and computationally robust methods to statistically derive the aforementioned values. Importantly, the deterministic models, which typically forecast net operating income volatility, are not statistically derived; so while Monte Carlo methods may be employed by such models to derive these values deterministically, such values are inconsistent with the actual default experience of CRELs. In addition, since such models do not include prepayment as a “competing” risk component in the hazard rate (to the extent a hazard rate model is used), they ignore a substantial empirical option risk embedded within CRELs. Furthermore, such models do not include the current delinquency status of loans that are known to contribute substantially to the probability of default estimates. Additionally, such models do not make an explicit provision to accommodate for the different treatment of rated CTLs. Finally, because non-traded instruments are used by such deterministic models in the determination of the above-mentioned values, such values cannot be used as the foundation for pricing the fair value of CMBS or for determining derivative risk measures for CMBS, such as its OAS without a risk-premium adjustment. This risk premium adjustment is nearly impossible to estimate and no one in portfolio theory has been able to accomplish such estimation for the past 30 years. Therefore, such deterministic models are limited in their use to industry and do not accomplish the application of OAS technology and risk-management practices to CMBS.
There is a vast literature related to prepayment modeling, OAS technology, and risk-management practices, and numerous collateral studies relating to both RMBS and CMBS. This literature discusses prepayment and OAS modeling techniques relating to the modeling of RMBS prepayment risks, which are substantially similar in theory to CMBS prepayment risks. With respect to CMBS, summary statistics on commercial mortgage defaults and loss severities from 1972-1997 have been provided and a default model for multifamily commercial mortgage has been studied. Competing risk hazard and prepayment models for CMBS have been estimated. None of these studies investigate valuation or hedging of CMBS. The valuation of a class of CMBS called “bullet” bonds has been studied and a structural model for CMBS valuation to determine such model's implications for tranche values has been simulated. However, those models have not been empirically tested. Despite all this literature and theoretical discussion, no empirically tested model for the evaluation of the risks of CMBS and CRELs has ever been published, and OAS technology still has not been adopted by the CMBS and CREL marketplace.
There is therefore a need to provide a process for introducing rational risk-management technology to participants in the CREL and CMBS markets to assist them in their risk management practices. There is a further need to establish continuity of affordable risk management technology to financial institutions investing in CRELs and CMBS, thereby elevating CMBS to the level of risk management practices enjoyed in the RMBS sector. Satisfying such needs may expand the audience of investors in CRELs and CMBS, by providing them with best practice risk management technology and thus enabling them to understand their risks better. As was the case in the residential mortgage market, satisfying such needs may bring greater efficiencies to the areas of lending, borrowing, and securities investing in United States CREL and CMBS markets.